Edge detection in a gray-scale image at a fine resolution typically yields noise and unnecessary detail, whereas edge detection at a coarse resolution distorts edge contours. We show that ``edge focusing'', i.e., a coarse-to-fine tracking in a continuous manner, combines high positional accuracy with good noise-reduction. This is of vital interest in several applications. Junctions of different kinds are in this way restored with high precision, which is a basic requirement when performing (projective) geometric analysis of an image for the purpose of restoring the three-dimensional scene. Segmentation of a scene using geometric clues like parallelism, etc., is also facilitated by the algorithm, since unnecessary detail has been filtered away. There are indications that an extension of the focusing algorithm can classify edges, to some extent, into the categories diffuse and nondiffuse (for example diffuse illumination edges). The edge focusing algorithm contains two parameters, namely the coarseness of the resolution in the blurred image from where we start the focusing procedure, and a threshold on the gradient magnitude at this coarse level. The latter parameter seems less critical for the behavior of the algorithm and is not present in the focusing part, i.e., at finer resolutions. The step length of the scale parameter in the focusing scheme has been chosen so that edge elements do not move more than one pixel per focusing step.